Your 0 ohm reading is the horn's electromagnet coil, not really 0 ohms (or it's really broken!) but fairly low. The 1.5K reading is across the switch contacts. To work, the electromagnet just pulls open the switch contacts and turns itself off, then the contacts spring back closed and turn it back on... this happens a few hundred times a second, making the horn sound.
Cleaning the contact points should revive your horn. You may need to bend the contact arm down a bit to increase the pressure on the contacts, this changes the tone of the horn though.